WASHINGTON -- To save on heating costs, Katherine Hackett of Moodus, Conn., sets her thermostat at 58 degrees and wears a hat and coat in the house. The mother of two military veterans, one who served in Afghanistan, she scrimps on food week by week.

Hackett was in the East Room of the White House Tuesday, beside President Barack Obama, as a representative and a symbol of the more than 1.3 million long-term jobless who have run out of unemployment benefits.

Will she get the money she needs to tide her over as she continues to search for work?

That's far from clear. It’s going to take a change of weather in Congress, where a polar vortex of cynicism, mistrust and hyper-partisanship has frozen compassion and blinded common sense.

If Obama, Democrats and Republicans in Congress can fashion a deal to extend long-term unemployment benefits, the result could presage a welcome -- and surprising -- period of cooperation. For now, though, everyone assumes the worst about everyone else’s motives, and election-year tactical thinking remains the default setting.

Take the issue of whether an extension of benefits needs a budgetary “pay for” -- that is, an equivalent amount of spending cuts (or revenue increases) specifically designated to pay for the benefits. Republicans are demanding just such a pay-for and in the form of spending cuts. Democrats’ refusal, so far, to formally offer any pay-for ideas is evidence, Republicans say, that the president and his party are just looking for a 2014 campaign issue -- and not a real deal on benefits.

“It’s going to be like this all year,” said a top GOP leadership aide in the Senate. “Democrats will be putting up legislation designed to fail.

“The UI [unemployment insurance] vote is a perfect example,” the aide said. “Pay for it, and it passes right away with a lot of bipartisan support. But they don’t even try.

“This is the year of bills designed to fail so that the HuffPost and others will have headlines reading, 'Republicans Block XX ...'”

Democrats counter that Republicans are being disingenuous and hypocritical, feigning concern for the unemployed even though their top priority is to assuage their anti-government tea party base. The Democrats cite history to make their case: President George W. Bush, who claimed to be a “compassionate conservative,” didn’t ask for pay-fors when he successfully sought emergency extended benefits in late 2002. And earlier in the Obama years, budget deals took extended benefits into account on a larger balance sheet, but didn't provide a separate cut of the kind the GOP is demanding now.

Acknowledging as much, Senate Minority Leader Mitch McConnell (R-Ky.) argues that the federal debt and deficit are now a more serious problem.

There's a chance -- faint for now -- that the combatants will back themselves into a benefits deal by posturing for political advantage: Democrats want to appear reasonable on the pay-for issue; Republicans don't want to seem cruel in the middle of winter.

Senate Democrats have offered to consider some pay-fors. Sen. Chuck Schumer of New York, for example, suggested that extended benefits could be tied to ending tax giveaways to companies that "ship jobs overseas." But he has to know that a tax increase is a non-starter.

Even less seriously, McConnell proposed offsetting the new spending by delaying or repealing the Obamacare individual mandate.

On Wednesday, Senate Majority Leader Harry Reid (D-Nev.) tried out for the unaccustomed role of Solomon, briefly.

"Let me start by saying that I am opposed to offsetting the cost of emergency unemployment benefits. The five times President Bush extended emergency unemployment insurance, we never offset the cost. And we should not offset it now, when there is still only one job available for every three people seeking work," said Reid. "That said, Democrats are not unreasonable. We are willing to discuss reasonable ways to pay for a long-term extension of emergency benefits."

But then he went back on offense: "If Republicans are so interested in paying for this measure, they should propose a reasonable way to do so -- one that doesn’t attack the Affordable Care Act or punish American children. They should propose an offset that might actually pass. Instead they proposed a string of political amendments, each more doomed to failure than the last.

Republicans, including House Speaker John Boehner (R-Ohio), have upped the ante by adding pet GOP ideas -- such as approval of the Keystone XL pipeline or delays in Obamacare -- to the unemployment bill.

Democrats “need to show a new openness to GOP bills that actually create jobs,” said a Boehner aide. “And to this point, they have shown no sign of doing that.”

As for the Democrats, they privately express confidence that they have the upper hand on the politics of unemployment benefits, no matter what the GOP does and no matter whether the bill ever passes.

“We have the issue,” said a Democratic consultant advising several 2014 Senate races. “If the Republicans agree, great. That seems unlikely. But either way, unemployment matters to our members -- and our voters.”

In other words, Katherine Hackett should keep the thermostat right where it is, at least for now.

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Swat team members secure the scene near Sparks Middle School in Sparks, Nev., after a shooting there on Monday, Oct. 21, 2013. Authorities are reporting that two people were killed and two wounded at the Nevada middle school. (AP Photo/Kevin Clifford)

Molly Delaney, left, holds her 11-year-old daughter, Milly Delaney, during a service in honor of the victims who died a day earlier when a gunman opened fire at Sandy Hook Elementary School in Newtown, Conn., as people gathered at St. John's Episcopal Church , Saturday, Dec. 15, 2012, in the Sandy Hook village of Newtown, Conn. The massacre of 26 children and adults at Sandy Hook Elementary school elicited horror and soul-searching around the world even as it raised more basic questions about why the gunman, 20-year-old Adam Lanza, would have been driven to such a crime and how he chose his victims.

Police secure the scene near Sparks Middle School after a shooting in Sparks, Nev., on Monday, Oct. 21, 2013. Authorities are reporting that two people were killed and two wounded at the Nevada middle school. (AP Photo/Kevin Clifford)

A security guard looks over the food court at the Clackamas Town Center mall as it opens, on Friday, Dec 14, 2012 in Portland, Ore. The mall is reopening, three days after a gunman killed two people and wounded a third amid a holiday shopping crowd estimated at 10,000. The shooter, Jacob Tyler Roberts, killed himself after the attack Tuesday afternoon.

Birmingham police arrive at the scene of a shooting at St. Vincent's Hospital on Saturday, Dec. 15, 2012 in Birmingham, Ala. Authorities in Alabama say a man opened fire the hospital, wounding an officer and two employees before he was fatally shot by police. Birmingham Police Sgt. Johnny Williams says the officer and employees suffered injuries that are not considered life-threatening.

Mourners attend the funeral and memorial service for the six victims of the Sikh temple of Wisconsin mass shooting in Oak Creek, Wis., Friday, Aug 10, 2012. The public service was held in the Oak Creek High School. Three other people were wounded in the shooting last Sunday at the temple. Wade Michael Page, 40, killed five men and one woman, and injured two other men. Authorities say Page then ambushed the first police officer who responded, shooting him nine times and leaving him in critical condition. A second officer then shot Page in the stomach, and Page took his own life with a shot to the head. (AP Photo/Jeffrey Phelps)

A policeman stands outside a Century 16 movie theater in Aurora, Colo., where a heavily armed man opened fire, killing at least 12 people and injuring 50 others.

Friends, family and employees react after a shooting at Cafe Racer in Seattle on May 30, 2012. A lone gunman killed four people Wednesday -- three were shot to death at a cafe, and a fourth in a carjacking. The gunman later killed himself.

Alameda County Community Food Bank workers move a memorial from a parking spot next to Oikos University in Oakland, Calif., Monday, April 23, 2012. Some students and staff members have arrived to resume class at Oikus University, the small California Christian college where seven people were shot to death earlier in April.

Panou Xiong, center, is comforted by family and friends following a Remembrance Ceremony commemorating the one-year anniversary of the worst mass shooting on a U.S. military base, where 13 people were killed and dozens wounded,, Nov. 5, 2010 in Fort Hood, Texas. Xiong's son, Pfc. Kham Xiong, was killed in the shooting.
CORRECTION: This slide originally said that the Fort Hood shooting took place in November 2010. The shooting took place in November 2009.

The charred Kinston, Ala. living room where suspected gunman Michael McLendon allegedly killed his mother Lisa McLendon, is photographed Wednesday, March 11, 2009. Authorities were working Wednesday to learn why a gunman set off on a rampage, killing 10 people across two rural Alabama counties.

An unidentified family member of slain Virginia Tech student Daniel Alejandro Prez Cueva, pauses at his memorial stone after the dedication of the memorial for the victims of the Virginia Tech shooting in Blacksburg, Va., Sunday, Aug. 19, 2007. More than 10,000 people gathered on the main campus lawn as Virginia Tech dedicated 32 memorial stones for those killed by a student in a mass shooting on campus last April.

This aerial shows the news media compound near Columbine High School in Littleton, Colo., April 21, 1999. Media from around the world poured into the area after 15 people were killed during a shooting spree inside the school.